1. Field of the Invention
The present invention generally relates to methods for obtaining geometrical models of the Earth surface, particularly, but not limitatively, for use in the planning of the coverage of radio communications network.
2. Description of the Related Art
Geometrical models of the Earth surface play an important role in fields like the radio communications network coverage planning, e.g. in mobile telecommunications systems like the UMTS (Universal Mobile Telecommunications System), or in broadcasting systems like the DVB-T (Digital Video Broadcasting-Terrestrial) and the DVB-H (Digital Video Broadcasting-Handheld), the latter being a digital video broadcasting over a mobile telecommunications network, the WiMAX.
Mainly, two classes of geometrical models of the Earth surface are known: the class of Digital Surface Models (DSMs), and that of Digital Terrain Models (DTMs).
A DSM provides a representation of the Earth's surface as it can be observed from above, typically from an airplane or a satellite, and contains indications of height, typically obtained by a telemetering system, related to the top of buildings and/or trees wherever the ground surface is not visible.
A DTM provides on the contrary indications about the elevation of the ground surface, also in areas where it is covered by buildings or trees.
In other words, both the DSM and the DTM are numeric representations of the height, but the DSM contains data related to the highest detected points of the metered objects, such as the top of trees, buildings and other man-made artifacts, and indicates the height of the ground surface only where it is not covered by objects; the DTM represents instead, in every point of the considered area, the height of the ground surface.
The DTMs can be derived from an analysis of the DSMs, by detecting objects located on the ground surface and, in that points, replacing the measured height with a derived height of the ground surface, as well as correcting errors (referred to as noise) in the DSMs caused by the data acquisition system.
Known methods for automatically converting DSMs into DTMs exploit additional information sources, like cadastral maps, which allow identifying areas covered by buildings and other man-made artifacts, or multi-spectra photography, which facilitates distinguishing among vegetation, roofs of buildings and other types of objects. For example, the article of C. Brenner et a/, “Fast production of virtual reality city models”, Proc. ISPRS, 1998, describes an approach that uses 2D ground plans and a laser DSM to derive 3D building geometry automatically, whereas texture is taken from terrestrial photographs; the main operations are: (a) the subdivision of the buildings' contours as they appear in the cadastral map into rectangles, (b) the association of each rectangle to a three-dimensional primitive, based on the analysis of the DSM, (c) the estimation of the parameters for each three-dimensional primitive, and (d) the union of the three-dimensional primitives for creating a model of the buildings.
Other methods known in the art for automatically converting DSMs into DTMs do not exploit additional information sources, but are based on the assumption that the noise in the DSM is very low; this assumption is reasonably close to the truth in DSMs obtained using the LIDAR (Light Detection And Ranging) technique. An example of this class of methods is provided by H. Gross et al, “3D-modeling of urban structures”, in Stilla U, Rottensteiner F, Hinz S (Eds) CMRT05, IAPRS, Vol. XXXVI, Part 3/W24, Vienna, Austria, Aug. 29-30, 2005; in that paper an automatic method is proposed for the generation of DTMs from high-quality DSMs obtained using LIDAR detection. Firstly, a gradient for the whole model is calculated; the points where the norm of the gradient exceeds a predetermined threshold are identified as “essential” points. The height is then interpolated linearly between the essential points, separately for the rows and the columns in the support of the model. The average of the two models, obtained by means of operations along the rows and the columns, is then filtered to obtain the DTM. Another example of this class of methods is provided in G. Forlani et a/, “Building reconstruction and visualization from LIDAR data”, The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol. XXXIV, Part 5/W12, 2003; in this case, LIDAR-acquired maps of limited width (800 m) are used; exploiting the high quality of the data, the buildings are identified thanks to the abrupt transition among the ground surface and the objects on it; a building is regarded as a volume enclosed between planes.
In case of DSMs characterized by high noise, and In absence of additional information sources like cadastral maps, the conversion of the DSM into the DTM is typically made manually or at most semi-automatically; in particular, a manual intervention is needed to identify points that can be designated as belonging to the ground surface. An example of this class of methods is provided in C. Baillard et a/, “3-D Reconstruction of Urban Scenes from Aerial Stereo Imagery: A Focusing Strategy”, Computer Vision and Image Understanding Vol. 76, No. 3, December, pp. 244-258, 1999: an iterative semi-automatic method is presented to produce DTMs starting from DSMs, with a manual initialization. The DSM is subdivided into disjoint patches, and the operator selects a point belonging to the ground surface for each patch. Then, the selected points are used as nodes or vertexes of a triangulation. The heights are then interpolated, obtaining a planar surface for each triangle. The DTM is then improved in an automatic way, searching the minimum of an energy function; during the execution, the nodes are classified as either “ground” or “not ground”.